1. Field of the Invention
This invention relates generally to the field of waveform analysis, and particularly in the exemplary embodiments to methods and apparatus for evaluating physiologic waveforms such as those present in the impedance cardiograms and electrocardiograms of a living subject.
2. Description of Related Technology
Time variant waveforms are commonplace in many technological disciplines. Analysis of such waveforms, including features or artifacts contained therein, can be useful for obtaining information regarding the waveform itself or the source of the waveform.
Waveform Analysis
A variety of techniques for waveform analysis are known under the prior art. One such technique is known as the “golden section search.” The golden section search is part of a larger class of analysis techniques referred to herein as “iterative interval” methods. The golden section search is a method of locating a maximum or minimum in a quantity or bracket of data. This technique involves evaluating the function at some point x in the larger of the two intervals (a,b), or (b,c). For location of the maximum, if f(x)>f(b) then x replaces the midpoint b, and b becomes an end point. If f(x)<f(b), then b remains the midpoint with x replacing one of the end points. Either way the width of the bracketing interval will reduce and the position of the minima will be better defined. FIG. 1 illustrates this process graphically, where the initial bracket (1,2,3) becomes (4,2,3), (4,2,5), and so forth.
The foregoing procedure is then repeated until the width achieves a desired tolerance. It can be shown that if the new test point, x, is chosen to be a given proportion (“golden section”) along the larger sub-interval, measured from the mid-point b, then the width of the full interval will reduce at an optimal rate. The golden section search advantageously requires no information about the derivative of the function itself. If such information is available it can be used to predict where best to choose the new point x in the above algorithm, leading to faster convergence.
Cardiovascular Analysis
One exemplary class of waveforms which are of significant interest are those generally relating to the cardiovascular function of living subjects. Included within this class of waveforms are electrocardiographs (ECGs) and impedance cardiographs (ICGs). As is well known, the study of the performance and properties of the cardiovascular system of a living subject has proven useful for diagnosing and assessing any number of conditions or diseases within that subject. The performance of the cardiovascular system, including the heart, has characteristically been measured in terms of several different parameters, including the stroke volume and cardiac output of the heart.
Noninvasive estimates of cardiac output (CO) can be obtained using the well known technique of impedance cardiography (ICG). Strictly speaking, impedance cardiography, also known as thoracic bioimpedance or impedance plethysmography, is used to calculate the stroke volume (SV) of the heart. As shown in Eqn. (1), when the stroke volume is multiplied by heart rate, cardiac output is obtained.CO=SV×heart rate.  (Eqn. 1)During impedance cardiography, a constant alternating current, with a frequency such as 70 kHz, I(t), is applied across the thorax. The resulting voltage, V(t), is used to calculate impedance. Because the impedance is assumed to be purely resistive, the total impedance, ZT(t), is calculated by Ohm's Law. The total impedance consists generally of a constant base impedance, Zo, and time-varying impedance, Zc(t), as shown in Eqn. 2:
                                          Z            T                    ⁡                      (            t            )                          =                                            V              ⁡                              (                t                )                                                    I              ⁡                              (                t                )                                              =                                    Z              o                        +                                                            Z                  c                                ⁡                                  (                  t                  )                                            .                                                          (                  Eqn          .                                          ⁢          2                )            The time-varying impedance is believed to reflect the change in resistance of the blood as it transverses through the aorta.
Stroke volume is typically calculated from one of three well known equations, based on this impedance change:
                                          Kubicek            ⁢                          :                        ⁢                                                  ⁢            SV                    =                                    ρ              ⁡                              (                                                      L                    2                                                        Z                    o                    2                                                  )                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (                  Eqn          .                                          ⁢          3                )            
                                          Sramek            ⁢                          :                        ⁢                                                  ⁢            SV                    =                                                    L                3                                            4.25                ⁢                                  Z                  o                                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (                  Eqn          .                                          ⁢          4                )            
                              Sramek          ⁢                      -                    ⁢          Bernstein          ⁢                      :                    ⁢                                          ⁢          SV                =                  δ          ⁢                                                    (                                  0.17                  ⁢                  H                                )                            3                                      4.25              ⁢                              Z                o                                              ⁢          LVET          ⁢                                                    ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                      .                                              (                  Eqn          .                                          ⁢          5                )            Where:                L=distance between the inner electrodes in cm,        LVET=ventricular ejection time in seconds,        Zo=base impedance in ohms,        
                                                        ⅆ                              Z                ⁡                                  (                  t                  )                                                                    ⅆ                              t                max                                              =                    ⁢                      magnitude            ⁢                                                  ⁢            of            ⁢                                                  ⁢            the            ⁢                                                                      ⁢                                                                    ⁢            largest            ⁢                                                  ⁢            negative            ⁢                                                  ⁢            derivative            ⁢                                                  ⁢            of            ⁢                                                  ⁢            the                                                                  ⁢                                    impedance              ⁢                                                          ⁢              change                        ,                                                                  ⁢                                                    Z                c                            ⁡                              (                t                )                                      ,                                                  ⁢                          occuring              ⁢                                                          ⁢              during              ⁢                                                          ⁢              systole              ⁢                                                          ⁢              in              ⁢                                                          ⁢              ohms              ⁢                              /                            ⁢              s                        ,                                                                        ρ            =                        ⁢                          resistivity              ⁢                                                          ⁢              of              ⁢                                                          ⁢              blood              ⁢                                                          ⁢              in              ⁢                                                          ⁢              ohms              ⁢                              -                            ⁢              cm                                ,                                                          H            =                        ⁢                          subject              ⁢                                                          ⁢              height              ⁢                                                          ⁢              in              ⁢                                                          ⁢              cm                                ,          and                                              δ          =                    ⁢                      special            ⁢                                                  ⁢            weight            ⁢                                                  ⁢            correction            ⁢                                                  ⁢                          factor              .                                          magnitude of the largest negative derivative of the impedance change,                Zc(t), occurring during systole in ohms/s,        ρ=resistivity of blood in ohms-cm,        H=subject height in cm, and        δ=special weight correction factor.Two key parameters present in Eqns. 3, 4, and 5 above are        
      (    i    )    ⁢            ⅆ              Z        ⁡                  (          t          )                            ⅆ              t        max            and (ii) LVET. These parameters are found from features referred to as fiducial points, that are present in the inverted first derivative of the impedance waveform,
      ⅆ          Z      ⁡              (        t        )                  ⅆ    t  . As described by Lababidi, Z., et al, “The first derivative thoracic impedance cardiogram,” Circulation, 41:651–658, 1970, the value of
      ⅆ          Z      ⁡              (        t        )                  ⅆ          t      max      is generally determined from the time at which the inverted derivative value has the highest amplitude, also commonly referred to as the “C point”. The value of
      ⅆ          Z      ⁡              (        k        )                  ⅆ          t      max      is calculated as this amplitude value. LVET corresponds generally to the time during which the aortic valve is open. That point in time associated with aortic valve opening, also commonly known as the “B point”, is generally determined as the time associated with the onset of the rapid upstroke (a slight inflection) in
      ⅆ          Z      ⁡              (        t        )                  ⅆ    t  before the occurrence of the C point. The time associated with aortic valve closing, also known as the “X point”, is generally determined as the time associated with the inverted derivative global minimum, which occurs after the C point.
In addition to the foregoing “B”, “C”, and “X” points, the so-called “O point” may be of mitral valve of the heart. The 0 point is generally determined as the time associated with the first peak after the X point. The time difference between aortic valve closing and mitral valve opening is known as the isovolumetric relaxation time, IVRT.
Impedance cardiography further utilizes the subject's electrocardiogram (ECG) in conjunction with the thoracic impedance waveform previously described. Processing of the impedance waveform for analysis generally requires the use of ECG fiducial points as landmarks. Processing of the impedance waveform is typically performed on a beat-by-beat basis, with the ECG being used for beat detection. In addition, detection of some fiducial points of the impedance signal may require the use of ECG fiducial points as landmarks. Specifically, individual beats are identified by detecting the presence of QRS complexes within the ECG. The peak of the R wave (commonly referred to as the “R point”) in the QRS complex is also detected, as well as the onset of depolarization of the QRS complex (“Q point”).
Historically, the aforementioned fiducial points in the impedance cardiography waveform (i.e., B, C, O, and X points) and ECG (i.e. R and Q points) were each determined through empirical curve fitting. However, such empirical curve fitting is not only labor intensive and subject to several potential sources of error, but, in the case of the impedance waveform, also requires elimination of respiratory artifact. More recently, digital signal processing has been applied to the impedance cardiography waveform for pattern recognition. One mathematical technique used in conjunction with such processing, the well known time-frequency distribution, utilizes complex mathematics and a well known time-frequency distribution (e.g., the spectrogram). See for example, U.S. Pat. Nos. 5,309,917, 5,423,326, and 5,443,073 issued May 10, 1994, Jun. 13, 1995, and Aug. 22, 1995, respectively, and assigned to Drexel University. As discussed in the foregoing patents, the spectrogram is used for extraction of information relating to the transient behavior of the dZ/dt signal. Specifically, a mixed time-frequency representation of the signal is generated through calculation of the Fast Fourier Transform and multiplication by a windowing function (e.g., Hamming function) to convert the one-dimensional discrete dZ/dt signal into a two-dimensional function with a time variable and frequency variable.
However, the spectrogram (and many of the time-frequency distributions in general) suffers from a significant disability relating to the introduction of cross term artifact into the pattern recognition calculations. Specifically, when a signal is decomposed, the time-frequency plane should accurately reflect this signal. If a signal is turned off for a finite time, some time-frequency distributions will not be zero during this time, due to the existence of interference cross terms inherent in the calculation of the distribution.
Another limitation of the spectrogram is its assumption of stationarity within the windowing function. This assumption is valid if the frequency components are constant throughout the window. However, many biological signals, including the ECG and the impedance waveform, are known to be non-stationary.
Additionally, the signal processing associated with such time-frequency distributions by necessity incorporates complex mathematics (i.e., involves operands having both real and imaginary components), which significantly complicates even simple pattern recognition-related computations.
Furthermore, such prior art empirical and time-frequency processing techniques impose substantial filtering requirements which can be restrictive in terms of hardware implementation. For example, the time delay associated with ΔZ waveforms may be large due to factors such as sharp frequency cutoffs required for empirical fiducial point detection.
It is also known that detection of right atrial and ventricular (AV) pacemaker spikes present in the ECG waveform may be useful in cardiovascular analysis. For example, when these spikes are detected, they may act as substitute Q points during definition of the search interval for B, C, and X points within the impedance waveform. Under the common prior art approach, such spikes are identified as a high frequency time derivative in ECG voltage that is larger than a fixed threshold voltage derivative. However, this detection scheme has several disabilities. Specifically, the technique is limited by the minimum spike amplitude that may be detected; i.e., only spikes of certain minimum amplitudes or greater may be detected. Furthermore, high amplitude noise may be misidentified as spikes, thereby reducing the robustness of the technique, especially in comparatively higher noise environments.
Fuzzy Logic and Fuzzy Models
As is well known in the art, so-called “fizzy logic” is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth; i.e., truth values falling between “completely true” and “completely false”. Fuzzy logic was invented by Dr. Lotfi Zadeh of U.C. Berkeley in 1965. The fuzzy model, which utilizes fuzzy logic, is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data systems. It can be implemented in hardware, software, or a combination of both. The fuzzy model provides a comparatively simple technique for arriving at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information, and in some aspects mimics the human decision making process.
As is well understood in the prior art, a fuzzy model incorporates alternative, rule-based mathematics (e.g., IF X AND Y THEN Z), as opposed to attempting to model a system or its response using closed-form mathematical equations. When the number of model inputs and model outputs are limited to two each, the fuzzy model is in general empirically-based, relying on an empirical data (such as prior observations of parameters or even an operator's experience).
Specifically, a subset U of a set S can be defined as a set of ordered pairs, each with a first element that is an element of the set S, and a second element that is an element of the set {0, 1}, with exactly one ordered pair present for each element of S. This relationship defines a mapping between elements of S and elements of the set {0, 1}. Here, the value “0” is used to represent non-membership, and the value “1” is used to represent membership. The truth or falsity of the exemplary statement:                A is in Uis determined by finding the ordered pair whose first element is A. The foregoing statement is true if the second element of the ordered pair is “1”, and the statement is false if it is “0”. Similarly, a fuzzy subset F of set S can be defined as a set of ordered pairs, each having a first element that is an element of the set S, and a second element that is a value falling in the interval [0, 1], with exactly one ordered pair present for each element of S. This defines a mapping between elements of the set S and values in the interval [0, 1]. The value zero is used to represent complete non-membership, the value one is used to represent complete membership, and values in between are used to represent intermediate degrees of membership. These fuzzy subsets serve as the fuzzy inputs and outputs of a fuzzy model, whose input-output relationship is defined by a rule base table.        
Inherent benefits of the fuzzy model relate to its speed and simplicity of processing (e.g., MIPS), and its ability to process data that is not easily represented in closed-form equations, such as may occur in physiologic data. However, prior to the present invention, these advantages have not been applied to the analysis of time-variant “noisy” signals where detection and/or identification of one or more artifacts within the waveform against a non-zero noise background of varying amplitude is required, such as electrocardiography, impedance cardiography, or electroencephalography.
Based on the foregoing, what is needed is an improved method and apparatus for waveform assessment, including for example identification of artifacts within electrocardiographs and thoracic impedance waveforms derived from a living subject. Such improved method and apparatus would ideally be accurate, easily adapted to the varying characteristics of different waveforms (and subjects), and would produce reliable results under a variety of different operating conditions and noise environments (i.e., robust). Additionally, such improved method and apparatus would utilize an analytical paradigm, such as fuzzy model, which would reduce the computational load associated with the analysis, thereby further simplifying use in various applications and hardware environments.